How do I properly thin a very thick mane? Do I thin from the underside or on the top side?

When thinning a horse’s mane, start with the longest hairs. Pulling the longest hairs will help get the mane to the desired length and thin the mane at the same time.
You will need a comb. If you are right-handed, take a small pinch of the longest mane in your left hand and with your right hand holding the comb, comb against the mane section you are holding to sort of tease the hair back. Then wrap the remaining hair you are holding in your left hand around the comb at least twice. Then pull the comb with a quick snap to pull the mane from the roots of the mane head.
If the mane is already short and even in length, it will be more difficult, but you can use the same technique. Be sure to pull the mane evenly along the horse’s mane from withers to poll. In this circumstance, you may find that you are pulling more hair from the underneath side.
Since you have indicated the horse has a very thick mane, you may need to thin in several short sessions. Trying to thin this horse’s mane adequately during one session may make the horse more tender and cause it to resent the mane-thinning process. You can alleviate this by taking your time and selecting very small sections to pull each time. This will also result in a more desirable mane and will avoid the pitfall of pulling larger sections/chunks of mane.
We suggest reviewing this video for a demonstration:
“Grooming for Success: Mane and Tail Care.”